no code implementations • 29 Jan 2019 • Puoya Tabaghi, Maarten de Hoop, Ivan Dokmanić
We study the learnability of a class of compact operators known as Schatten--von Neumann operators.
no code implementations • 18 May 2020 • Puoya Tabaghi, Ivan Dokmanić
Hyperbolic space is a natural setting for mining and visualizing data with hierarchical structure.
no code implementations • 17 Jun 2020 • Puoya Tabaghi, Jianhao Peng, Olgica Milenkovic, Ivan Dokmanić
To study this question, we introduce the notions of the \textit{ordinal capacity} of a target space form and \emph{ordinal spread} of the similarity measurements.
no code implementations • 7 Feb 2021 • Puoya Tabaghi, Ivan Dokmanic
Congruent Procrustes analysis aims to find the best matching between two point sets through rotation, reflection and translation.
1 code implementation • 21 Oct 2022 • Samantha Chen, Puoya Tabaghi, Yusu Wang
For measures supported in discrete metric spaces, finding the optimal transport distance has cubic time complexity in the size of the space.
no code implementations • 20 Oct 2023 • Puoya Tabaghi, Yusu Wang
Restricting the domain of the functions to finite multisets of $D$-dimensional vectors, Deep Sets also provides a \emph{universal approximation} that requires a latent space dimension of $O(N^D)$ -- where $N$ is an upper bound on the size of input multisets.
1 code implementation • 19 Feb 2021 • Puoya Tabaghi, Chao Pan, Eli Chien, Jianhao Peng, Olgica Milenkovic
The results show that classification in low-dimensional product space forms for scRNA-seq data offers, on average, a performance improvement of $\sim15\%$ when compared to that in Euclidean spaces of the same dimension.
2 code implementations • 30 Mar 2024 • Zhishang Luo, Truong Son Hy, Puoya Tabaghi, Donghyeon Koh, Michael Defferrard, Elahe Rezaei, Ryan Carey, Rhett Davis, Rajeev Jain, Yusu Wang
Using the input and output data of the tools from past designs, one can attempt to build a machine learning model that predicts the outcome of a design in significantly shorter time than running the tool.
1 code implementation • 19 May 2022 • Eli Chien, Puoya Tabaghi, Olgica Milenkovic
Furthermore, it is currently not known how to choose the most suitable approximation objective for noisy fitting.
1 code implementation • 8 Sep 2021 • Eli Chien, Chao Pan, Puoya Tabaghi, Olgica Milenkovic
For hierarchical data, the space of choice is a hyperbolic space since it guarantees low-distortion embeddings for tree-like structures.
1 code implementation • 7 Mar 2022 • Chao Pan, Eli Chien, Puoya Tabaghi, Jianhao Peng, Olgica Milenkovic
The excellent performance of the Poincar\'e second-order and strategic perceptrons shows that the proposed framework can be extended to general machine learning problems in hyperbolic spaces.
1 code implementation • 6 Jan 2023 • Puoya Tabaghi, Michael Khanzadeh, Yusu Wang, Sivash Mirarab
Finding a low-dimensional Riemannian affine subspace for a set of points in a space form amounts to dimensionality reduction because, as we show, any such affine subspace is isometric to a space form of the same dimension and curvature.